Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #441 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,4,5,3)(10,12,14,20)(11,15,17,18)(13,22,21,19)(16,25,24,23);(6,8,9,7)(12,19)(13,21)(15,23)(16,24)(18,25)(20,22);(2,3)(4,5)(6,7,9,8)(10,11,14,17)(12,18,20,15)(13,16,21,24)(19,25,22,23)Polycyclic presentation:
2^6,5|a^2=e,b^2=ef,c^2=f,d^2=f,c^a=cf,g^a=g^4,c^b=cd,d^b=df,d^c=df50 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#65078, #10610505, #10610541, … |
| maximal normal subgroup of | C2×#65078, #10610505, #10610541, … |
| maximal quotient of | #10599008, #10599014, #10599015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 416);